Orbitals are considered to have the same energy when their wavefunctions have the same value for a given energy level. Here are some conditions under which orbitals can have the same energy:
Hydrogen-like atoms: In the case of a hydrogen atom or hydrogen-like atoms (such as singly ionized helium), the orbitals within a given energy level, characterized by the principal quantum number (n), have the same energy. For example, in the n=2 energy level, the 2s and 2p orbitals have the same energy.
Spherical symmetry: In spherically symmetric systems, such as an isolated atom, the orbitals with the same value of the principal quantum number (n) but different values of the azimuthal quantum number (l) have the same energy. For instance, in the n=3 energy level, the 3s, 3p, and 3d orbitals have the same energy.
Degenerate orbitals: As mentioned in the previous response, certain symmetries or interactions can lead to degeneracy, resulting in orbitals with the same energy. For example, in highly symmetric molecules or systems with certain symmetries, orbitals can be degenerate, meaning they have the same energy.
It's important to note that in more complex systems, such as molecules or multi-electron atoms, the energy levels and orbital energies can be influenced by various factors, including electron-electron interactions, molecular geometry, and external fields. These factors can lead to the splitting of energy levels and break the degeneracy of orbitals.